integral of cos((pix)/2)+picos(x)

Lösung

\int cos (\frac{π x}{2}) + π cos (x) d x

\frac{2}{π} sin (\frac{π x}{2}) + π sin (x) + C

Schritte zur Lösung

\int cos (\frac{π x}{2}) + π cos (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (\frac{π x}{2}) d x + \int π cos (x) d x

\int cos (\frac{π x}{2}) d x = \frac{2}{π} sin (\frac{π x}{2})

\int π cos (x) d x = π sin (x)

= \frac{2}{π} sin (\frac{π x}{2}) + π sin (x)

Füge eine Konstante zur Lösung hinzu

= \frac{2}{π} sin (\frac{π x}{2}) + π sin (x) + C

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